Filter coefficients can be optimized according to many different criterium. For example stop band attenuation, coding gain, degree of smoothness can be used as the criterium to optimize a filter. However, solving for these optimal filter coefficients requires solving a time domain problem that is a non-linear constrained optimization problem that can be difficult to solve. In order to optimize these coefficients requires solving the non-linear constrained optimization equations iteratively to arrive at the optimum solutions. However, this iterative process is computationally expensive due to the difficulty of solving the equations. In addition, if the constraints are not satisfied then the solution is not invertible.
Therefore, it would be advantageous to provide a method for solving for the optimal parameters for a filter that is not constrained and is more efficient computationally than the time domain problem.